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ARTICLE

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

by Muhammad Farman^1,2,4, Ali Akgül^3,9,*, Mir Sajjad Hashemi⁵, Liliana Guran^6,7, Amelia Bucur^8,*

1 Institue of Mathematics, Khwaja Fareed University of Enginnering and Information Technology, Raheem Yar Khan, Pakistan
2 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3 Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, 56100, Turkey
4 Department of Mathematics, Mathematics Research Center, Near East University, Nicosia, Turkey
5 Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey
6 Department of Hospitality Services, Babes-Bolyai University, Cluj-Napoca, 400174, Romania
7 Department of Pharmaceutical Sciences, Vasile Goldiș Western University of Arad, Arad, 310025, Romania
8 Department of Mathematics and Informatics, Faculty of Sciences, Lucian Blaga University of Sibiu, Sibiu, 550012, Romania
9 Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

* Corresponding Authors: Ali Akgül. Email: ; Amelia Bucur. Email:

(This article belongs to the Special Issue: Recent Developments on Computational Biology-I)

Computer Modeling in Engineering & Sciences 2024, 138(2), 1385-1403. https://doi.org/10.32604/cmes.2023.028803

Received 08 January 2023; Accepted 09 June 2023; Issue published 17 November 2023

Abstract

New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model’s Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation.

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